\[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
Test:
NMSE p42, negative
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Time: 11.5 s
Input Error: 16.0
Output Error: 16.0
Log: ⚲
Profile: 🕒
\(\frac{\left(-b\right) + \left(-\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}{2 \cdot a}\)
  1. Started with
    \[\frac{\left(-b\right) - \sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
    16.0
  2. Using strategy rm
    16.0
  3. Applied add-cube-cbrt to get
    \[\frac{\left(-b\right) - \color{red}{\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a} \leadsto \frac{\left(-b\right) - \color{blue}{{\left(\sqrt[3]{\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}\right)}^3}}{2 \cdot a}\]
    16.8
  4. Using strategy rm
    16.8
  5. Applied sub-neg to get
    \[\frac{\color{red}{\left(-b\right) - {\left(\sqrt[3]{\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}\right)}^3}}{2 \cdot a} \leadsto \frac{\color{blue}{\left(-b\right) + \left(-{\left(\sqrt[3]{\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}\right)}^3\right)}}{2 \cdot a}\]
    16.8
  6. Applied simplify to get
    \[\frac{\left(-b\right) + \color{red}{\left(-{\left(\sqrt[3]{\sqrt{{b}^2 - 4 \cdot \left(a \cdot c\right)}}\right)}^3\right)}}{2 \cdot a} \leadsto \frac{\left(-b\right) + \color{blue}{\left(-\sqrt{{b}^2 - \left(4 \cdot a\right) \cdot c}\right)}}{2 \cdot a}\]
    16.0

Original test:


(lambda ((a default) (b default) (c default))
  #:name "NMSE p42, negative"
  (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))
  #:target
  (if (< b 0) (/ c (* a (/ (+ (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a)))) (/ (- (- b) (sqrt (- (sqr b) (* 4 (* a c))))) (* 2 a))))